Theory and simulations of rigid polyelectrolytes

TL;DR

This paper combines theoretical analysis and molecular dynamics simulations to study stiff polyelectrolytes, revealing conditions where mean-field theory fails and exploring effects like effective attraction due to multivalent counterions.

Contribution

It provides a comprehensive comparison of Poisson-Boltzmann theory, correlation corrections, and simulations for stiff polyelectrolytes, including new insights into ion correlations and osmotic behavior.

Findings

Osmotic coefficient can become negative with multivalent counterions.

Mean-field Poisson-Boltzmann theory can fail quantitatively and qualitatively.

Ion-ion correlations are significant in the strong coupling regime.

Abstract

We present theoretical and numerical studies on stiff, linear polyelectrolytes within the framework of the cell model. We first review analytical results obtained on a mean-field Poisson-Boltzmann level, and then use molecular dynamics simulations to show, under which circumstances these fail quantitatively and qualitatively. For the hexagonally packed nematic phase of the polyelectrolytes we compute the osmotic coefficient as a function of density. In the presence of multivalent counterions it can become negative, leading to effective attractions. We show that this results from a reduced contribution of the virial part to the pressure. We compute the osmotic coefficient and ionic distribution functions from Poisson-Boltzmann theory with and without a recently proposed correlation correction, and also simulation results for the case of poly(para-phenylene) and compare it to recently obtained experimental data on this stiff polyelectrolyte. We also investigate ion-ion correlations in the strong coupling regime, and compare them to predictions of the recently advocated Wigner crystal theories.